The ability of the marine controlled source electromagnetic method to resolve anisotropy in the sediment conductivity is not very well understood. In this study, we address the resolvability of anisotropy using a Bayesian approach. Two markedly different methods, slice sampling and reversible jump Markov Chain Monte Carlo have been used for the Bayesian inversion of a synthetic model of a resistive oil reservoir trapped beneath the seabed. We use this to identify which components of data can provide the strongest constraints on anisotropy in the overburden, reservoir and underlying sediments.